Sensitivity analysis of stationary performance measures for Markov chains

Derivative estimation is an important problem in performance analysis of discrete event dynamic systems. Derivative estimation of stationary performance measures is difficult since it generally requires the consistency of estimators. aper proposes an algorithm for derivative estimation of stationary performance measures for Markov chains. Both discrete-time and continuous-time chains are considered. The basic idea is to simulate the original Markov chain with a modified performance measure which can be estimated by extra simulations. The computational load of the extra simulations at each step is bounded. It is shown under mild assumptions that the algorithm attains the best possible rate of convergence as the simulation time goes to infinity. An unexpected connection between the algorithm and solutions to Poisson equations is also revealed.